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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p><dfn class="terminology">Example 2</dfn>For</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
(1-x^2) y^{\prime \prime}-2 x y^{\prime}+\alpha (\alpha+1) y=0,
\end{equation*}
</div>
<p class="continuation">where <span class="process-math">\(\alpha\)</span> is a constant. Is <span class="process-math">\(x=1\)</span> an ordinary point or singular point?<dfn class="terminology">Solution:</dfn></p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\frac{Q(x)}{P(x)}=\frac{-2 x}{1-x^2},
\end{equation*}
</div>
<p class="continuation">which is not continuous at <span class="process-math">\(x=1\text{.}\)</span> The Taylor series does not exist at this point, thus <span class="process-math">\(x=1\)</span> is a singular point.</p>
<span class="incontext"><a href="sec5_2.html#p-209" class="internal">in-context</a></span>
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